The U-WEDGE Transformation Method for Multivariate Geostatistical Simulation

Mathematical Geosciences

Volumn 44, Issue 4, 2012, Pages 427-448

  Mueller, Ute A ^a   Ferreira, Jacqueline ^a  

^a EDITH COWAN UNIVERSITY   (Australia)

Author keywords

Joint approximate diagonalisation; MAF; Spatial decorrelation

Indexed keywords

AUTOCORRELATION FACTOR; COSIMULATION; DATA SETS; GEOSTATISTICAL SIMULATION; JOINT APPROXIMATE DIAGONALISATION; MAF; SEMIVARIOGRAMS; SPATIAL DECORRELATION; SPATIAL STRUCTURE; SYMMETRIC MATRICES; TRANSFORMATION METHODS; VARIANCE/COVARIANCE;

IRON ORES;

COMPUTER SIMULATION; CORRELATION; GEOSTATISTICS; IRON ORE; MATRIX; MULTIVARIATE ANALYSIS; NUMERICAL MODEL; SPATIAL ANALYSIS; VARIOGRAM;

EID: 84860917624     PISSN: 18748961     EISSN: 18748953     Source Type: Journal    
DOI: 10.1007/s11004-012-9384-7     Document Type: Article

References (25)

1. Afsari B (2006) Sensitivity analysis for the problem of matrix joint diagonalisation. SIAM J Matrix Anal Appl 30: 1148-1171.
2. Bandarian EM (2008) Linear transformation methods for multivariate geostatistical simulation. Dissertation, Edith Cowan University, 148 p.
3. Bandarian EM, Bloom LM, Mueller UA (2008) Direct minimum/maximum autocorrelation factors for multivariate simulation. Comput Geosci 34: 190-200. doi: 10. 1016/j. cageo. 2007. 03. 015.
4. Bandarian EM, Mueller UA (2008) Reformulation of MAF as a generalised eigenvalue problem. In: Ortiz J, Emery X (eds) Proceeding of the eighth international geostatistics congress, Santiago, Chile, pp 1173-1178.
5. Bandarian EM, Mueller UA, Ferreira J, Richardson S (2010) Transformation methods for multivariate geostatistical simulation-minimum/maximum autocorrelation factors and alternating columns-diagonal centres. In: Dimitrakopoulos R (ed) Advances in orebody modelling and strategic mine planning I. Spectrum Series, vol 17.
6. Boucher A, Dimitrakopoulos R (2009) Block-support simulation of multiple correlated variables. Math Geosci 41: 215-237.
7. Bunse Gerstner A, Byers R, Mehrmann V (1993) Numerical methods for simultaneous diagonalisation. SIAM J Matrix Anal Appl 14: 927-949.
8. Cardoso JK, Souloumiac A (1996) Jacobi angles for simultaneous diagonalisation. SIAM J Matrix Anal Appl 17: 161-164.
9. Desbarats JA, Dimitrakopoulos R (2000) Geostatistical simulation of regionalized pore-size distributions using Min/Max autocorrelation factors. Math Geol 32: 919-942.
10. Ferreira J (2010) Comparison and application of three decorrelation methods PCA, MAF and ACDC. BSc (Hons) Mathematics Thesis, Edith Cowan University, Australia.
11. Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York.
12. Lopes JA, Rosas CF, Fernandes JB, Vanzela GA (2011) Risk quantification in grade tonnage curves and resource categorization in a lateritic Nickel deposit using geologically constrained joint conditional simulation. J Min Sci 47: 166-176.
13. Manton JH (2005) A centroid (Karcher mean) approach to the joint approximate diagonalisation problem: the real symmetric case. Digit Signal Process 16: 465-478. doi: 10. 1016/j. dsp. 2005. 06. 003.
14. Pham TD (2001) Joint approximate diagonalisation of positive definite matrices. SIAM J Matrix Anal Appl 22: 1136-1152.
15. Rondon O, Tran TT (2008) Multivariate simulation using min/max autocorrelation factors: practical aspect and case studies in the mining industry. In: Ortiz J, Emery X (eds) Proceeding of the eighth international geostatistics congress, Santiago, Chile, pp 269-278.
16. Switzer P, Green AA (1984) Min/Max autocorrelation factors for multivariate spatial imaging. Stanford University, Palo Alto.
17. Tichavsky P, Yeredor A (2009) Fast approximate joint diagonalization incorporating weight Matrices. IEEE Trans Signal Process 57: 878-891.
18. Tercan AE (1999) Importance of orthogonalization algorithm in modelling conditional distributions by orthogonal transformed indicator methods. Math Geol 31: 155-174.
19. Tran TT, Murphy M, Glacken I (2006) Semivariogram structures used in multivariate conditional simulation via minimum/maximum autocorrelation factors. In: Proceedings XI international congress, IAMG, Liège.
20. Vargas-Guzman JA, Dimitrakopoulos R (2003) Computational properties of min/max autocorrelation factors. Comput Geosci 29: 715-723.
21. Vollgraf R, Obermayer K (2006) Quadratic optimization for simultaneous matrix diagonalization. IEEE Trans Signal Process 54: 3270-3278.
22. Wackernagel H (2003) Multivariate geostatistics, 3rd rev edn. Springer, Berlin.
23. Yeredor A (2002) Non orthogonal joint diagonalization in the least square sense with application in blind source separation. IEEE Trans Signal Process 50: 645-648.
24. Xie T, Myers DE, Long AE (1995) Fitting matrix-valued variogram models by simultaneous diagonalization (Part II: Application). Math Geol 27: 877-888.
25. Ziehe A, Laskov P, Nolte G, Müller KR (2004) A fast algorithm for joint diagonalisation with non-orthogonal transformations and its application to blind source separation. J Mach Learn Res 5: 777-800.